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Research Papers

Power Analysis of Epicyclic Transmissions Based on Constraints

[+] Author and Article Information
Chao Chen

Department of Mechanical and Aerospace Engineering,  Monash University, Clayton, Victoria, 3800 Australiachao.chen@monash.edu

The dimensions are derived from Table 2 in Ref. [3]. The dimensions do not reflect the real size of the powertrain, since only kinematics relations are in interests. Some dimensions are modified in order to maintain geometric constraints.

The loss factor used here is a simplification of the actual phenomena, from the kinematic point of view. Mechanical power losses can be dependent on operating conditions, lubricant parameters, temperature, and contact surface roughness.

It is important to mention that this total efficiency only considers load-dependent losses. If other power loss components including drag and viscous are considered, this efficiency should be lower. Further, this is a numerical example and not a true prediction for this transmission since the values of these loss factors are not from experiments. Experimental data on spur, helical, hypoid, and planetary gear efficiency, for example [8], can be much lower than the ones used in this paper.

J. Mechanisms Robotics 4(4), 041004 (Sep 04, 2012) (11 pages) doi:10.1115/1.4007308 History: Received December 19, 2011; Revised March 31, 2012; Published August 31, 2012; Online September 04, 2012

Epicyclic gear transmissions have many applications. The internal power flow of epicyclic systems is highly related to the power loss of the system. A systematic method and generic formulas based on kinematic constraints are derived to conduct the power flow analysis, by means of Lagrange multipliers and newly introduced selection matrices. The method and formulas can be readily applied to complicated epicyclic systems. The graphic representation of the power flow of two examples verifies the balance of the power flow and virtual power flow. In the example of the Dual-E powertrain for hybrid electrical vehicles, an estimation of the total efficiency is derived. The pattern of contour maps of the total efficiency indicates the operational ranges of the powertrain with relatively low power losses.

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Copyright © 2012 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Two bodies constrained at a single point P

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Figure 2

Notations for (a) a bearing connection and (b) a gearing mesh

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Figure 3

A simple one-dof epicyclic train

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Figure 4

Power flow of the simple epicyclic train

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Figure 5

Schematic drawing of Dual-E powertrain [3]

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Figure 6

Power flow of Dual-E powertrain

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Figure 7

The total efficiency of the Dual-E powertrain with respect to α and β, when (a) all the loss factors are 0.1, (b) all the loss factors are 0.1 except l4=0.2, (c) all the loss factors are 0.1 except l5=0.2, and (d) all the loss factors are 0.1 except l9=0.2

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